Sampling Distributions

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Chapter 6

• Sampling Distributions

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Definitions

• Parameter- a numerical descriptive measure of a
  population
• Sample statistic- a numerical descriptive measure
  of a sample taken from the population.
• Sampling taking many samples each one of size
  n.
• Sampling Distribution- the probability
  distribution of the statistic.

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Mean, Variance, Std. Dev. Of Sampling Distribution
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Properties of Sampling Distributions Section 6.2
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Homework-Section 6.1, 6.3

• Consider the population described by the
  probability distribution shown here
• If you have 5 items and you want to choose 2, how
  many ways can you do so?

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Possible Samples from Population
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Probability Distribution for the Sample Mean
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Section 6.2 Page 272, 6.10

• Consider the probability distribution shown here

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6.10 continued

• A)

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6.10 continued

• For a random sample of n 3 observations from
  this distribution, find the sampling distribution
  of the sample mean.
• There will be 27 samples

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Mean of the Means
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c) Find the sampling distribution of the median
of a sample of n3 from this population
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d) Refer to b) and c) and show that mean and
median are unbiased estimators of the true mean
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Central Limit Theorem

• If a random sample of n observations is selected
  from a poulation (any population) with mean,
• Then when n is sufficiently large, the sampling
  distribution of
• will be an approximately normal distribution. The
  larger the sample size, the better will be the
  normal approximation to the sampling distribution
  of

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Point Estimator

• A point estimator of a population parameter is a
  rule or formula that tells us how to use the
  sample data to calculate a single number that can
  be used as an estimate of the population
  parameter.
• E.g. Take the sample, find the mean of the
  sample, and use that sample mean to estimate the
  population mean.

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Estimate Bias

• A point estimate is unbiased if its expected
  value is equal to the value of the parameter it
  is intended to estimate.

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6.16 page 279

• Suppose a random sample of n 25 measurements is
  selected from a population with mean 10 and
  standard deviation 3, find

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6.30 Pages 280-281

• A study in Psychological Assessment reported a
  mean of 4.59 and standard dev. of 2.95. Assume
  these are the correct parameters for this
  population. Would you expect to observe a sample
  mean of 6 or higher?

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Homework- Chapter 6

• Pages 267-268, 6.1,6.2,6.3
• Pages 272-273, 6.10,6.14
• Pages 279-281, 6.15,6.16,6.17,6.18,6.30

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Error of Estimation

• The difference between the point estimate and the
  true value of the parameter.

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Standard Error of the Statistic

• The standard deviation of the sampling
  distribution is also called the standard error.
• Standard error